Answer: (a) y = -3x + 10
[tex]\bold{(b)\x=\bigg(\dfrac{10}{3},0\bigg)}[/tex]
Step-by-step explanation:
The slope of line CD is perpendicular to line OB, which means they have opposite and reciprocal slopes.
Step 1: Find the slope of OB using the formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
(x₁, y₁) = (0, 0) and (x₂, y₂) = (3, 1)
[tex]m=\dfrac{1-0}{3-0} = \dfrac{1}{3}[/tex]
Step 2: Find the slope of CD (opposite and reciprocal of OB)
[tex]m = \dfrac{1}{3}\qquad m_\perp=-\bigg(\dfrac{3}{1}\bigg) = -3[/tex]
Step 3: Input the perpendicular slope and the slope into the Point-Slope formula: y - y₁ = m(x - x₁)
(x₁, y₁) = (3, 1) because it is the point the line will pass through
y - 1 = -3(x - 3)
y - 1 = -3x + 9 distributed -3 into (x - 3)
y = -3x + 10 added 1 to both sides
***********************************************************************
The x-intercept of DQ is the same x-intercept as CD. The x-intercept is when y = 0
y = -3x + 10
0 = -3x + 10
-10 = -3x subtracted 10 from both sides
[tex]\dfrac{10}{3}=x[/tex] divided both sides by -3
