fill in the missing variables in the slope-intercept form, y = mx + b to write the equation of the line passing through the points (1,1) and (3,5).

Question

Another way to write the equation is

Answer 1

To find the equation of the line passing through the points (1, 1) and (3, 5), we will first calculate the slope (m) using the formula:

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

where $(x_1,y_1)=(1,1)$ and $(x_2,y_2)=(3,5)$:

$$m=\frac{5-1}{3-1}=\frac{4}{2}=2$$

Now that we have the slope $m=2$, we can use one of the points to find the y-intercept (b) using the slope-intercept form of a line, $y=mx+b$. We will use the point (1, 1):

$$1=2(1)+b$$

This simplifies to:

$$1=2+bb=1-2b=-1$$

Now that we have both the slope and the y-intercept, we can write the equation of the line:

$$y=2x-1$$

So, to summarize, the slope-intercept form of the equation for the line passing through the points (1, 1) and (3, 5) is:

$$y=2x-1$$

Another way to write the equation is in point-slope form, which would be:

$$y-y_1=m(x-x_1)$$

Using point (1, 1), this gives:

$$y-1=2(x-1)$$

Either form accurately represents the same line.