Question

WILL GIVE BRAINLIEST WORTH THIRTY POINTS! Find a so that CD will have the given slope: a) C(5,−2), D(−4,a); m=0 b) C(a,–1), D(–3,2); m=undefined c) C(–3,–2), D(1,a); m=2

Answer 1

The value of a for the equation of line CD are;

• a) a = -2

• b) a = -3

• c) a = 6

Given the following data:

a) C(5, -2), D(-4, a); m = 0

• Point on x-axis ($x_{1}, x_{2}$) = $5, -4$

• Point on y-axis ($y_{1}, y_{2}$) = $-2, a$

• Slope, m = 0

To find the value of a;

Mathematically, the slope (m) of an equation of line is given by the formula;

$Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the values into the formula, we have;

$0 = \frac{a - [-2]}{-4 - 5}\\\\0 = \frac{a\; + \;2}{-9}$

Cross-multiplying, we have;

$-9$ × $0$ = $a + 2$

$a +2 = 0$

a = -2

b) C(a, -1), D(-3, 2); m = undefined

• Point on x-axis ($x_{1}, x_{2}$) = $a, -3$

• Point on y-axis ($y_{1}, y_{2}$) = $-1, 2$

• Slope, m = undefined

To find the value of a;

Note: Undefined is a terminology used to refer to a mathematical expression that has not been assigned a value or isn't correct. Also, a mathematical expression is considered to be undefined when its denominator is zero (0) i.e it is divided by zero (0).

Substituting the given values into the slope formula, we have;

Undefined $= \frac{2 - [-1]}{-3 - a}$

Undefined $= \frac{2 + 1}{-3 - a}$

Next, we would equate the denominator to zero (0);

$-3 - a = 0$

a = -3

c) C(-3, -2), D(1, a); m = 2

• Point on x-axis ($x_{1}, x_{2}$) = $-3, 1$

• Point on y-axis ($y_{1}, y_{2}$) = $-2, a$

• Slope, m = 2

Substituting the values into the formula, we have;

$2 = \frac{a - [-2]}{1 - [-3]}\\\\2 = \frac{a\; + \;2}{1 \;+ \;3}\\\\2 = \frac{a\; + \;2}{4}$

Cross-multiplying, we have;

$4$ × $2$ = $a + 2$

$a +2 = 8$

$a = 8 -2$

a = 6

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