Question

What equation in slope-intercept form represents the line that passes through
the points (1,3) and (2,5)?

Answer 1

Answer:

So, equation in slope-intercept form that represents the line that passes through  the points (1,3) and (2,5) is y=2x+1

Step-by-step explanation:

We need to write equation in slope intercept form that represents the line that passes through  the points (1,3) and (2,5)

The standard equation of slope-intercept form is: y= mx+b

where m is the slope of the lines and b is the y-intercept.

To make the equation we need to find slope (m) and y-intercept (b)

Find Slope

The formula to find slope m is: $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

We have $x_{1}=1, x_{2}=2, y_{1}=3\ and \ y_{2}=5$

Putting values in the formula to find slope

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\m=\frac{5-3}{2-1}\\m=\frac{2}{1}\\m=2$

So, value of slope m is m=2

Find y-intercept

Using formula of slope-intercept formula we can find b

y=mx+b

Using point (1,3) (where x=1 ,y=3) and slope m=2

$3=2(1)+b\\3=2+b\\b=3-2\\b=1$

So, value of y-intercept b is: b=1

Required equation in Slope Intercept Form

We have slope m = 2 and y-intercept b=1

$y=mx+b\\y=2x+1$

So, equation in slope-intercept form that represents the line that passes through  the points (1,3) and (2,5) is y=2x+1