Question

How do you find slope and intercepts to graph $y=-\dfrac{2}{3}x-1$ ?

Answer 1

Hint: In this question, we have to find the slope and intercepts of the equation and then plot the equation using them. Thus, we use the slope-intercept form. As we know that, the slope is the ratio of the vertical change or horizontal change between any two distinct points on the curve. About intercepts, the x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. Thus, we see the given equation is similar to the line of the equation $y=mx+c$ . Therefore, on comparing both the equations, we get the value of the slope of the equation and the intercepts. Then, we will draw the graph of the equation using the slope and intercepts, which is our required answer.

Complete answer:
In this question, we have to plot the equation using the slope-intercept form.
As we know, the general equation of the line is $y=mx+c$ ------- (2)
m is the slope of the equation = $\dfrac{y}{x}=\dfrac{\text{rise}}{\text{run}}$ , means you will go vertically and x will go horizontal
In addition, c is the y-intercept = constant
And, the equation given to us is $y=-\dfrac{2}{3}x-1$ ------------- (1)
Therefore, we see the equation (2) and (1) are similar to each other.
Thus, on comparing equations (1) and (2), we get that
the slope of the equation $y=-\dfrac{2}{3}x-1$ = $m=-\dfrac{2}{3}$ , and
the intercept of y-axis $y=-\dfrac{2}{3}x-1$ = $c=-1$ .
So, now we will draw a graph using slope $m=-\dfrac{2}{3}$ and y-intercept $c=-1$ or $c=\left( 0,-1 \right)$ , that is
First, we plot the y-intercept $c=\left( 0,-1 \right)$ of the equation, we get
Now, we will plot the slope of the equation $m=-\dfrac{2}{3}$ , which is we raise 2 units from the y-intercept and then run 3 units towards the negative x-axis, we get

Now, we join points A and C, to get the required line of equation, that is

Thus, we draw the graph of equation $y=-\dfrac{2}{3}x-1$ with slope $m=-\dfrac{2}{3}$ and y-intercept $c=-1$ or $c=\left( 0,-1 \right)$.

Note: Always do proper calculations to get the exact slope and intercept of the equation. Whenever you get fractional intercept, try making them in decimal, it will help you better to draw the graph. You can also find the y-intercept by using the substitution method. Let x=0 in the equation and solve for y, which is the required y-intercept for the answer.