Graph the line having a slope of − 4 -4 and passes through ( − 1 , 5 ) \left(-1,5\right) .

This problem asks us to graph the line having a slope of negative four that passes through the point negative one five. Now what I notice is that I have a point which is given, negative one five, and I have my slope which is negative four. Now my first step is going to be plotting this point negative one five. You can see on my graph we have an x of negative one, and for an x of negative one would be back here, and then a y value of five, meaning this is where our point would lie. So we have our point negative one, five plotted. Now next, we have this slope of negative four. Remember that slope is rise divided by run. So So I can also write this as negative four divided by one. So that means is our rise is gonna be negative four. Since the negative value, that means we're actually going to go down. So I'm gonna go down one, two, three, four units, which would put me right about here, and then I also need to run to the right one. So then from this point, we would go to the right one. So we go down four to the right one, and that lands us right there on the y axis at this point, which would be zero one. So notice that we now have our points plotted. We figured this out from our slope, and that will allow us to get our line. And then if we can connect this line through these points here, this will give us the answer to our problem. So this is how you can graph lines when you are given the point and the slope.

4. Graphing

Slope of a Line

Beginning Algebra

4. Graphing

Slope of a Line

Struggling with Beginning Algebra?

Join thousands of students who trust us to help them ace their exams!

Multiple Choice

Graph the line having a slope of $negative 4$ and passes through $open paren negative 1 comma 5 close paren$ .

Graph showing a line with slope -4 passing through the point (-1, 5) on a Cartesian coordinate plane.

Graph of a line with slope -4 passing through the point (-1, 5) on a coordinate plane.

Verified step by step guidance

Step 1: Identify the given slope and point. The slope is $-4$ and the point the line passes through is $(-1, 5)$.

Step 2: Use the point-slope form of a line equation: $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is the point. Substitute $m = -4$, $x_1 = -1$, and $y_1 = 5$ to get $y - 5 = -4(x + 1)$.

Step 3: To graph the line, start by plotting the point $(-1, 5)$ on the coordinate plane.

Step 4: Use the slope $-4$ which means a change in $y$ of $-4$ for every change in $x$ of \$1$. From the point $(-1, 5)$, move right 1 unit (increase $x$ by 1) and down 4 units (decrease $y$ by 4) to find a second point.

Step 5: Draw a straight line through the two points. This line represents the graph of the equation with slope $-4$ passing through $(-1, 5)$.

5:13m

Watch next

Master Finding the Slope of a Line with a bite sized video explanation from Patrick Ford

Struggling with Beginning Algebra?

Graph the line having a slope of −4-4 and passes through (−1,5)\(\left\)(-1,5\(\right\)).

Watch next

Graph the line having a slope of $negative 4$ and passes through $open paren negative 1 comma 5 close paren$ .