Question

A line passes through the points (2,4) and (-4,-1). Find its equation in slope-intercept form. (2 points, 1 for work, 1 for equation)

Answer 1

Hello!

The answer is:

The equation of the line in slope-intercept form:

$y=\frac{5}{6}x+\frac{7}{3}$

Why?

To find the equation in slope-intercept form, we need to follow the next steps:

Find the slope of the line:

Using the slope formula, we have:

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

We are given the points:

$(2,4)\\(-4,-1)$

So, substituting we have:

$m=\frac{(-1)-(4)}{-4-2}$

$m=\frac{-5}{-6}$

$m=\frac{5}{6}$

Find the "b" value:

Now that we know the value of the slope, we can write the equation of the line:

$y=\frac{5}{6}x+b$

In order to find "b" we need to substituite any of the given points, we know that line is thru both of the given points, so, substituting (2,4) we have:

$4=\frac{5}{6}*2+b\\\\4=\frac{10}{6}+b\\\\4=\frac{5}{3}+b\\\\b=4-\frac{5}{3}=\frac{(3*4)-5}3}=\frac{12-5}{3}=\frac{7}{3}$

Now that we know the slope and "b", we can write the equation of the line in slope-intercept form:

$y=\frac{5}{6}x+\frac{7}{3}$

Have a nice day!