Question

How do you write the equation of the line going through the point (1, 7) parallel to the x-axis?

Answer 1

Hint:
 The above question is a simple question of linear equations in two variables. The general equation of the slope-intercept form of the line is given as y = mx + c, where m is the slope of the line and c is the y-intercept of the line. Also, note that when a line is parallel to x-axis then its slope is equal to 0, so the equation of such line is given as y = a where a is the y-intercept that line.

Complete step by step answer:
We can see from the question that we are provided with a line that is parallel to the x-axis.
Since we know that when a line is parallel to the x-axis then its slope equal to 0.
Also, we know that the slope-intercept form of the line is given by y = mx + c, where m is the slope of the line and c is the y-intercept of the line.
So, we can say that equation of the line is equal to $ y=0\times x+c $
 $ \Rightarrow y=c $
Now, we know from the question that the line y = c passes through the point (1, 7).
So, the point (1, 7) will satisfy the line y = c.
 $ \Rightarrow 7=c $
Hence, c =7.
So, y = 7 is the equation of the line passing through the point (1, 7) which is parallel to the x-axis.

This is the required solution.
Note:
Students are required to note that general equation of the line is given as $ \left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right) $ where m is the slope of the line, and $ \left( {{y}_{1}},{{x}_{1}} \right) $ is the point through which the line passes. We know that the line given in the question is parallel to x-axis, so slope of the line is equal to 0 and since the line passes through the point (1, 7), hence the equation of line will be:
 $ \Rightarrow \left( y-7 \right)=0\times \left( x-1 \right) $
 $ \therefore y=7 $ is the equation of the required line.