Answer:
[tex]y=\frac{9}{4}x-\frac{55}{4}[/tex]
Step-by-step explanation:
Slope-intercept form: y = mx + b
Slope formula: [tex]\frac{y2-y1}{x2-x1}[/tex]
Given points: (3, -7), (7, 2)
(3, -7) = (x1, y1)
(7, 2) = (x2, y2)
To write the equation in slope-intercept form, we need to find the slope(m) and the y-intercept(b) of the equation.
First, let's find the slope. To do this, input the given points into the slope formula:
[tex]\frac{2-(-7)}{7-3}[/tex]
Simplify:
2 - (-7) = 2 + 7 = 9
7 - 3 = 4
[tex]\frac{9}{4}[/tex]
The slope is [tex]\frac{9}{4}[/tex].
To find the y-intercept, input the slope and one of the given points(in this example I'll use point (7, 2)) into the equation and solve for b:
[tex]2=\frac{9}{4}(7)+b[/tex]
[tex]2=\frac{63}{4}+b[/tex]
[tex]-\frac{55}{4} =b[/tex]
The y-intercept is [tex]-\frac{55}{4}[/tex].
Now that we know the slope and the y-intercept, we can write the equation:
[tex]y=\frac{9}{4}x-\frac{55}{4}[/tex]
