Question

How do you find slope and intercept of graph \[y = 4x + 9\] ?

Answer 1

Hint: Generally the slope intercept form is \[y = mx + c\] where m is the slope of the line and c is the y intercept. So we can compare with standard form to get the slope and intercept of the given graph.

Complete step-by-step answer:
Given \[y = 4x + 9\]
First we will check whether it is in standard form or not. is not then we will arrange the terms so that it is in standard form and then compare.
But here it is already in standard form. So we will compare directly with the standard form of slope intercept.
So the slope of the given graph is clearly what we can say is \[m = 4\] .
Now for intercepts we will assign the x and y to zeros to get y and x intercepts respectively.
First we will find x intercept.
Putting y equals to zero in the given equation of line we get,
 \[\Rightarrow 0 = 4x + 9\]
On transposing the terms,
 \[\Rightarrow 4x = - 9\]
Taking 4 on other side of equation we get,
 \[\Rightarrow x = \dfrac{{ - 9}}{4}\]
This is the x intercept.
And for y intercept we know in the slope intercept form the term c is the y intercept. So it is 9.
This slope is \[m = 4\] , x intercept is \[x = \dfrac{{ - 9}}{4}\] and y intercept is \[y = 9\] .
This is our answer.
So, the correct answer is “ \[m = 4\] , x intercept is \[x = \dfrac{{ - 9}}{4}\] and y intercept is \[y = 9\] ”.

Note: Note that writing the given equation in slope intercept form is simply a procedure of steps to be followed. If we are given two points of coordinate system lying on a line then we also can find the slope of the line. That equation involves slope and intercept. That’s it!
Slope is the ratio of vertical change to horizontal change. If the line is increasing then slope is positive and if line is decreasing then slope is negative. Also note that in geometrical cases the slope is given with the help of tan function.