Question

What is the slope and y-intercept of \[4x + y = 7\] ?

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. We convert the given equation into the slope intercept form and we compare it to get the desired result.

Complete step by step solution:
Given,
 \[4x + y = 7\] .
Now rearranging \[4x + y = 7\]
 \[ \Rightarrow y = - 4x + 7\] .
Now we have slope intercept form with slope m and y-intercept ‘c’ is \[y = mx + c\] . On comparing \[ \Rightarrow y = - 4x + 7\] this with the general form we have,
Slope \[m = - 4\] and y-intercept \[c = 7\]
Additional information:
We can also find the y-intercept by putting the value of x is equal to zero.
Put \[x = 0\] in \[4x + y = 7\]
 \[4(0) + y = 7\]
 \[y = 7\] . Thus the y-intercept is 7.
To find the x-intercept substitute the value of ‘y’ is zero the,
Put \[y = 0\] in \[4x + y = 7\]
 \[4x + 0 = 7\]
 \[4x = 7\]
 \[x = \dfrac{7}{4}\] . This is the x-intercept.

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 the positive x-axis.