Question

How do you find the intercepts for $ y = 7x + 3 $ ?

Answer 1

Hint: In the given question, we are required to find the intercepts for the line represented by the equation $ y = 7x + 3 $ . The given problem involves the concepts of straight lines and different forms of writing the equations representing straight lines. We convert the given equation to the intercept form. Then comparing the simplified equation with the general intercept form of the equation, we will get the desired result.

Complete step by step solution:
We know the equation of a line having the x intercept as ‘a’ and y intercept as ‘b’ is given by $ \dfrac{x}{a} + \dfrac{y}{b} = 1 $ .
So, we have to manipulate the given equation representing the straight line so as to match the intercept form of the line. Hence, we have,
 $ y = 7x + 3 $
Shifting $ 7x $ from right side of the equation to left side of the equation using the transposition rule, we get,
 $ \Rightarrow y - 7x = 3 $
Dividing both sides of the equation by $ 3 $ , we get,
 \[ \Rightarrow \dfrac{{y - 7x}}{3} = 1\]
Distributing the denominator to both the fractions individually, we get,
 \[ \Rightarrow \dfrac{y}{3} - \dfrac{{7x}}{3} = 1\]
Manipulating the equation so as to match with the intercept form of the equation of straight line, we get,
 \[ \Rightarrow \dfrac{y}{{\left( 3 \right)}} - \dfrac{x}{{\left( {\dfrac{3}{7}} \right)}} = 1\]
Adjusting the negative sign between the two terms, we get,
 \[ \Rightarrow \dfrac{y}{{\left( 3 \right)}} + \dfrac{x}{{\left( {\dfrac{{ - 3}}{7}} \right)}} = 1\]
Now, comparing the equation \[\dfrac{y}{{\left( 3 \right)}} + \dfrac{x}{{\left( {\dfrac{{ - 3}}{7}} \right)}} = 1\] with the general intercept form of the equation for straight line $ \dfrac{x}{a} + \dfrac{y}{b} = 1 $ , we get,
X intercept of the line is $ - \dfrac{3}{7} $ and Y intercept of the line is $ 3 $ .
So, the correct answer is “X intercept of the line is $ - \dfrac{3}{7} $ and Y intercept of the line is $ 3 $ ”.

Note: Manipulation of the given equation should be done to an extent where the equation remains unchanged and represents the same straight line on the graph paper. Care should be taken while executing the calculative steps.