Question

#2) Write an eq of the line that passes through the points (-4, -1) and (-1, 11) in slope intercept form

Answer 1

To find the equation of the line in slope-intercept form that passes through (-4, -1) and (-1, 11), calculate the slope (m = 4) and then use one of the points to solve for the y-intercept (b = 15), resulting in y = 4x + 15.

Step-by-step explanation:

To write the equation of the line that passes through the points (-4, -1) and (-1, 11) in slope-intercept form, we first find the slope of the line using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the values in, we get m = (11 - (-1)) / (-1 - (-4)) = 12 / 3 = 4. Next, we use one of the points to find the y-intercept. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Substituting the slope and the coordinates of one point into this equation, we get -1 = 4(-4) + b. Simplifying gives us b = -1 + 16 = 15. Hence, the equation of the line is y = 4x + 15.

Answer 2

The Slope-Intercept form of the equation of a line is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

You can find the slope of the line with this formula:

`m=(y_2-y_1)/(x_2-x_1)`

For this case you can set up that:

`\begin{gathered} y_2=-1 \\ y_1=11 \\ x_2=-4 \\ x_1=-1 \end{gathered}`

Substituting values into the formula, you get that the slope of this line is:

`m=(-1-11)/(-4-(-1))=(-12)/(-4+1)=(-12)/(-3)=4`

Substitute the slope and one of the coordinates of one of the points on the line, into the equation

`y=mx+b`

And solve for "b":

`\begin{gathered} -1=4(-4)+b \\ -1=-16+b \\ -1+16=b \\ b=15 \end{gathered}`

Therefore, knowing "m" and "b", you can determine that the equation of this line in Slope-Intercept form is:

`y=4x+15`