Students gain practice writing equations in slope-intercept form from graphs in this eighth-grade algebra worksheet! In this two-page practice worksheet, students are asked to find the slope and y-intercept of graphed lines and write the equation of those lines in slope-intercept form. Understanding how to write equations in slope-intercept form will help students to model linear relationships and solve real-world problems involving linear relationships. Students can get practice with other representations of linear functions by completing Write Equations in Slope-Intercept Form From Tables and Writing Equations in Slope-Intercept Form: Review. GradeSubjectView aligned standardsProblem 1 : Graph the line with slope -2 and y-intercept 4. Problems 2-5 : Write the equation that describes each line in slope-intercept form. Problem 2 : Slope = 2/5, y-intercept = 6. Problem 3 : Slope = 0, y-intercept = -4. Problem 4 : Problem 5 : Slope = 4, (2, 5) is on the line. Problems 6-8 : Write each equation in slope-intercept form. Then graph the line described by the equation. Problem 6 : 4x - y - 3 = 0 Problem 7 : 2x + 3y - 6 = 0 Problem 8 : 3x + 2y = 8 Problem 9 : To rent a vehicle, a moving company charges $30.00 plus $0.50 per mile. The cost as a function of the number of miles driven is shown in the graph. Problem 10 : A caterer charges a $200 fee plus $18 per person served. The cost as a function of the number of guests is shown in the graph. Answers1. Answer : Step 1 : The y-intercept is 4, so the line contains (0, 4). Plot (0, 4). Step 2 : Slope = change in y / change in x = -2/1 Count 2 units down and 1 unit right from (0, 4) and plot another point. Step 3 : Draw the line through the two points. 2. Answer : Write the slope-intercept form equation of a line : y = mx + b Substitute 2/5 for m and 6 for b. y = (2/5)x + 6 y = 2x/5 + 6 3. Answer : Write the slope-intercept form equation of a line : y = mx + b Substitute 0 for m and -4 for b. y = (0)x + (-4) y = 0 - 4 y = -4 4. Answer : Step 1 : Find the y-intercept. The graph crosses the y-axis at (0, 1), so b = 1. Step 2 : Find the slope. The line contains the points (0, 1) and (1, 3). Use the slope formula. m = (y2 - y1) / (x2 - x1) Substitute (0, 1) for (x1 , y1) and (1, 3) for (x2 , y2). m = (3 - 1) / (1 - 0) m = 2/1 m = 2 Step 3 : Write the slope-intercept form equation of a line : y = mx + b Substitute 2 for m and 1 for b. y = 2x + 1 5. Answer : Step 1 : Find the y-intercept. Write the slope-intercept form equation of a line : y = mx + b Substitute 4 for m, 2 for x, and 5 for y. 5 = 4(2) + b 5 = 8 + b Subtract 8 from each side. -3 = b Step 2 : Write the slope-intercept form equation of a line : y = mx + b Substitute 4 for m and -3 for b. y = 4x + (-3) y = 4x - 3 6. Answer : Step 1 : Write the given equation slope-intercept form : 4x - y - 3 = 0 Add y to each side. 4x - 3 = y y = 4x - 3 y = 4x - 3 is in the form y = mx + b. Slope : m = 4 = 4/1 y-intercept : b = -3 Step 2 : Plot (0, -3). Step 3 : Count 4 units up and 1 unit right and plot another point. Step 4 : Draw the line connecting the two points. 7. Answer : Step 1 : Write the given equation slope-intercept form : 2x + 3y - 6 = 0 Subtract 2x from each side and add 6 to each side. 3y = -2x + 6 Divide each side 3. 3y/3 = (-2x + 6)/3 y = -2x/3 + 6/3 y = (-2/3)x + 2 Slope : m = -2/3 y-intercept : b = 2 Step 2 : Plot (0, 2). Step 3 : Count 2 units down and 3 unit right and plot another point. Step 4 : Draw the line connecting the two points. 8. Answer : Step 1 : Write the given equation slope-intercept form : 3x + 2y = 8 Subtract 3x from each side and add 6 to each side. 2y = -3x + 8 Divide each side 2. 2y/2 = (-3x + 8)/2 y = -3x/2 + 8/2 y = (-3/2)x + 4 Slope : m = -3/2 y-intercept : b = 4 Step 2 : Plot (0, 4). Step 3 : Count 3 units down and 2 unit right and plot another point. Step 4 : Draw the line connecting the two points. 9. Answer : Part (i) : Cost is $0.50 per mile times miles plus $30.00. y
= 0.50x + 30 An equation is y = 0.5x + 30. Part (ii) : The y-intercept is 30. This is the cost for 0 miles, or the initial fee of $30.00. The slope is 0.5. This is the rate of change of the cost : $0.50 per mile. Part (iii) : y = 0.5x + 30 Substitute 150 for x in the equation. = 0.5(150) + 30 = 75 + 30 = 105 The cost of the vehicle for 150 miles is $105. 10. Answer : Part (i) : Cost is $18 per guest plus $200. y = 18x + 200 An equation is y = 18x + 200. Part (ii) : The y-intercept is 200. This is the cost for 0 guests, or the initial fee of $200. The slope is 18. This is the rate of change of the cost : $18 per guest. Part (iii) : y = 18x + 50 Substitute 200 for x in the equation. = 18(200) + 200 = 3600 + 200 = 3800 The cost of catering for 200 guests is $3800. Kindly mail your feedback to We always appreciate your feedback. ©All rights reserved. onlinemath4all.com How do I write an equation in slopeThe slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). It's usually easy to graph a line using y=mx+b. Other forms of linear equations are the standard form and the point-slope form. Equations of lines have lots of different forms.
What is the slope of the line given the equation 4x 2y 8?Using the slope-intercept form, the slope is 2 .
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