Question

Given the points (4,-2) and (8,1), what is the equation of a line that connect the two points. Answer in slope-intercept form.

Answer 1

The equation of required line in slope-intercept form is:

$y=\frac{3}{4}x-5$

Step-by-step explanation:

We are given the points (4,-2) and (8,1) we need to find the equation of a line that connect the two points. We need to find equation of line in slope-intercept form.

The standard equation of slope-intercept form is:

$y=mx+b$

m is slope and b is y-intercept

• Finding slope:

Using formula: $Slope=\frac{y_2-y_1}{x_2-x_1}$

Putting values:

x_1=4, y_1=-2, x_2=8 and y_2=1

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

$Slope=\frac{1-(-2)}{8-4}$

$Slope=\frac{1+2}{4}$

$Slope=\frac{3}{4}$

So slope is: $Slope=\frac{3}{4}$

• Now finding y-intercept:

Using point (4,-2) and slope $Slope=\frac{3}{4}$

$y=mx+b\\-2=\frac{3}{4}(4)+b\\-2=3+b\\b=-2-3\\b=-5$

So, value of y-intercept is -5

The equation of required line is:

$y=mx+b\\y=\frac{3}{4}x-5$

So, the equation of required line in slope-intercept form is:

$y=\frac{3}{4}x-5$

Keywords: Equation of line using Slope  

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