Question

What is the slope and intercept of \[y = \dfrac{1}{3}x + 3\]?

Answer 1

Hint: We will use the general equation of a line which is given by \[y = mx + c\]. That is the slope intercept form. Here ‘m’ is called slope and ‘c’ is called y-intercept. To find the x- intercept we put y value as zero in the given equation. We convert the given equation into the slope intercept form and we compare it to get the desired result.

Complete step-by-step solutions:
Given,
\[y = \dfrac{1}{3}x + 3\].
Now we have slope intercept form with slope m and y-intercept ‘c’ is \[y = mx + c\]. On comparing\[ \Rightarrow y = \dfrac{1}{3}x + 3\] this with the general form we have,
Slope \[m = \dfrac{1}{3}\] and y-intercept \[c = 3\]
To find the x-intercept substitute the value of ‘y’ is zero the,
Put \[y = 0\] in \[y = \dfrac{1}{3}x + 3\]
\[0 = \dfrac{1}{3}x + 3\]
\[\dfrac{1}{3}x = - 3\]
\[x = - 3 \times 3\]
\[x = - 9\]. This is the x-intercept.
Additional information:
We can also find the y-intercept by putting the value of x is equal to zero.
Put \[x = 0\] in \[y = \dfrac{1}{3}x + 3\]
\[y = \dfrac{1}{3}(0) + 3\]
\[y = 3\]. Thus the y-intercept is 3.

Note: We know that x and y intercept basically refer to the points where the line cuts the x-axis and y-axis of the graph. The point where coordinate cuts the line at x-axis is x-intercept and y-axis is y-intercept. We know that the slope of a line is basically the tangent of the angle the line makes with positive x-axis.