Question

my hw write find an equation of the line passing through (-2,3) and (4,-5) I have to write the equation in slope-intercept form I need help

Answer 1

Answer:

The line passing through the given points is:

$y=-\frac{4}{3}x+\frac{1}{3}$

in its slope-intercept form

Step-by-step explanation:

Start by finding the slope of the segment that joins the two given points using the slope formula:

$slope=\frac{y_2-y_1}{x_2-x_1}$

which for our case renders:

$slope=\frac{3-(-5)}{-2-4}=\frac{8}{-6} =-\frac{4}{3}$

Now we can find the y-intercept by using any one of the given points in the general slope-intercept form of a line with this slope:

$y=-\frac{4}{3} x+b\\3=-\frac{4}{3} (-2)+b\\3=\frac{8}{3}+b\\b=3-\frac{8}{3} \\b=\frac{9-8}{3} \\b=\frac{1}{3}$

Therefore, the equation of the line becomes:

$y=-\frac{4}{3}x+\frac{1}{3}$