Question

Use point-slope or slope-intercept form to match the equations in slope-intercept form with the given slope m and

point (x, y).
m = 3; point (1, -3)
m = 3; point (4, 5)
m = 3; point (-2, 1)
y = 3x-6
y = 3x - 7
y = 3x + 7

Answer 1

The equations y = 3x - 6, y = 3x - 7, and y = 3x + 7 match the points (1, -3), (4, 5), and (-2, 1) respectively with a slope m = 3 for all, by solving for the y-intercept using the given slope and point.

Step-by-step explanation:

The equations of lines in slope-intercept form follow the formula y = mx + b, where m is the slope and b is the y-intercept. To match the given slopes and points with the equations, we will use the slope and a single point to solve for b and rewrite the equation in its slope-intercept form.

1. 
   
2. For the slope m = 3 and point (1, -3), plug the values into the slope-intercept form: y = mx + b becomes -3 = 3(1) + b. Solving for b gives us b = -6. Thus, the equation is y = 3x - 6.
3. 
   
4. For the slope m = 3 and point (4, 5), plug the values into the same form: 5 = 3(4) + b. Solving for b gives us b = -7. Hence, the equation is y = 3x - 7.
5. 
   
6. Finally, for the slope m = 3 and point (-2, 1), plug the values in: 1 = 3(-2) + b. Solve for b to get b = 7. The corresponding equation is y = 3x + 7.

Each point and slope pair uniquely determines the y-intercept and the equation of the line in slope-intercept form.