Question

1. draw a line through the point such that the value of the y - intercept is the same as the value of the x - intercept.

Explanation:

Step1: Assume the intercept form of the line

The intercept form of a line is \(\frac{x}{a}+\frac{y}{a}=1\) (since \(x - intercept=a\) and \(y - intercept=a\)), which can be rewritten as \(y=-x + a\)

Step2: Find the value of \(a\)

We assume the point through which the line passes is \((- 10,0)\). Substitute \(x=-10\) and \(y = 0\) into \(y=-x + a\)
\(0=-(-10)+a\)
\(0 = 10+a\)
\(a=-10\)

Step3: Write the equation of the line

The equation of the line is \(y=-x - 10\)

To draw the line:

• The \(x - intercept\): set \(y = 0\), then \(0=-x - 10\), \(x=-10\)
• The \(y - intercept\): set \(x = 0\), then \(y=-0 - 10=-10\)
• Plot the points \((-10,0)\) and \((0,-10)\) and draw a straight line through them

Answer:

Draw a line passing through \((-10,0)\) and \((0,-10)\)