Find the value of a if the line joining the points (3a,4) and (a-3) has a gradient of 1
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Answers
Answer:
a=
2
7
or 3.5
Step-by-step explanation:
We have the two points (3a, 4) and (a, -3).
And we want to find the value of a such that the gradient of the line joining the two points is 1.
Recall that the gradient or slope of a line is given by the formula:
\displaystyle m=\frac{y_2-y_1}{x_2-x_1}m=
x
2
−x
1
y
2
−y
1
Where (x₁, y₁) is one point and (x₂, y₂) is the other.
Let (3a, 4) be (x₁, y₁) and (a, -3) be (x₂, y₂). Substitute:
\displaystyle m=\frac{-3-4}{a-3a}m=
a−3a
−3−4
Simplify:
\displaystyle m=\frac{-7}{-2a}=\frac{7}{2a}m=
−2a
−7
=
2a
7
We want to gradient to be one. Therefore, m = 1:
\displaystyle 1=\frac{7}{2a}1=
2a
7
Solve for a. Rewrite:
\displaystyle \frac{1}{1}=\frac{7}{2a}
1
1
=
2a
7
Cross-multiply:
2a=72a=7
Therefore:
\displaystyle a=\frac{7}{2}\text{ or } 3.5a=
2
7
or 3.5