Question

what is the slope-intercept equation of the line that goes through the points 1, 5 and 2, 8​

Answer 1

Answer:

The slope-intercept equation of the line that goes through the points (1, 5) and (2, 8) is​ $\mathbf{y=\frac{3}{2}x+\frac{7}{2} }$

Step-by-step explanation:

We need to find the slope-intercept equation of the line that goes through the points (1, 5) and (2, 8)

The general equation for slope intercept form is ​ $y=mx+b$ where m is slope and b is y-intercept

Finding slope

Slope can be found using formula $Slope=\frac{y_2-y_1}{x_2-x_1}$

We have $x _1=1, y_1=5, x_2=2, y_2=8$

Putting values and finding slope

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{8-5}{2-1}\\Slope=\frac{3}{2}$

So, we get slope $m=\frac{3}{2}$

Finding y-intercept

y-intercept can be found using slope $m=\frac{3}{2}$ and point (1,5)

$y=mx+b\\5=\frac{3}{2}(1)+b\\b=5- \frac{3}{2}\\b=\frac{10-3}{2}\\b=\frac{7}{2}$

So, we get y-intercept $b=\frac{7}{2}$

Equation of line

So, equation of line having slope $m=\frac{3}{2}$ and y-intercept $b=\frac{7}{2}$ is:

$y=mx+b\\y=\frac{3}{2}x+\frac{7}{2}$

The slope-intercept equation of the line that goes through the points (1, 5) and (2, 8) is​ $\mathbf{y=\frac{3}{2}x+\frac{7}{2} }$