Answer:
Point-slope form: [tex]y-5 = \frac{4}{5} (x-3)[/tex]
Slope-intercept form: [tex]y = \frac{4}{5} x+\frac{13}{5}[/tex]
Step-by-step explanation:
1) First, find the slope of the equation with the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of the given points into the formula and solve:
[tex]m = \frac{(1)-(5)}{(-2)-(3)} \\m = \frac{1-5}{-2-3} \\m = \frac{-4}{-5} \\m = \frac{4}{5}[/tex]
2) We now have enough information to write the equation in point-slope form. Point-slope form is represented by the formula [tex]y-y_1 = m (x-x_1)[/tex]. Substitute real values for the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
[tex]m[/tex] represents the slope, so substitute [tex]\frac{4}{5}[/tex] for it. The [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line intersects. So, pick any of the two given points (either one is fine, both outcomes would represent the same line) and substitute its x and y values into the formula as well. (I chose (3,5), as seen below.) This gives the following equation in point-slope form:
[tex]y-5 = \frac{4}{5} (x-3)[/tex]
3) Now, convert the equation above to slope-intercept form, represented by the formula [tex]y = mx + b[/tex]. Isolate y to find the following equation in slope-intercept form:
[tex]y-5=\frac{4}{5}(x-3)\\y-5 = \frac{4}{5} x-\frac{12}{5} \\y = \frac{4}{5} x-\frac{12}{5} +5\\y = \frac{4}{5} x-\frac{12}{5} +\frac{25}{5} \\y = \frac{4}{5} x+\frac{13}{5}[/tex]
