Question

How do you find the x-intercept of $ 4x - 3y = 12 $ ?

Answer 1

Hint: We have given an equation of a line as $ 4x - 3y = 12 $ , which is a straight-line equation. A straight-line equation is always linear and represented as $ y = mx + c $ where $ m $ is the slope of the line and $ c $ is the y-intercept and $ \dfrac{{ - c}}{m} $ is the x-intercept .

Complete step-by-step solution:
We have equation of line,
  $ 4x - 3y = 12 $
Now, Add $ 4x $ both the side ,
 $ \Rightarrow - 3y = 12 + 4x $
Now multiply by $ - \dfrac{1}{3} $ to both the side of the equation,
 $ \Rightarrow y = - 4 - \dfrac{4}{3}x $
Or
 $ \Rightarrow y = - \dfrac{4}{3}x - 4 $
Now we compare this given equation with the general linear equation i.e., $ y = mx + c $
Hence ,
Slope of the given line, $ m = - \dfrac{4}{3} $ .
y-intercept of the given line , $ c = - 4 $ .
Therefore, we can say that point $ (0, - 4) $ lies on the line.
x-intercept of the given line , $ \dfrac{{ - c}}{m} = \dfrac{{ - ( - 4)}}{{ - \left( {\dfrac{4}{3}} \right)}} = - 3 $ .
Therefore, we can say that point $ ( - 3,0) $ lies on the line.

Additional Information:
i) Slope of a line can also be found if two points on the line are given . let the two points on the line be $ ({x_1},{y_1}),({x_2},{y_2}) $ respectively.
Then the slope is given by , $ m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} $ .
ii) Slope is also defined as the ratio of change in $ y $ over the change in $ x $ between any two points.
 y-intercept can also be found by substituting $ x = 0 $ .
iii) Similarly, x-intercept can also be found by substituting $ y = 0 $ .

Note: This type of linear equations sometimes called slope-intercept form because we can easily find the slope and the intercept of the corresponding lines. This also allows us to graph it.
We can quickly tell the slope i.e., $ m $ the y-intercepts i.e., $ (y,0) $ and the x-intercept i.e., $ (0,y) $ .we can graph the corresponding line.