QUESTION 7
iii
Easy
Draw the graph of the following equations, and identify their slopes and y-intercepts. Also, find the coordinates of the points where these lines cut the y-axis.
\(5y = 6x − 10\)
SOLUTION
1
Find slope and y-intercept from the given equation
\(5y = 6x − 10\)
⇒ \(y = \frac{6}{5}x − \frac{10}{5}\)
⇒ \(y = 1.2x − 2\)
Here, slope \(= 1.2\) and \(y-\)intercept \(= −2 \)
The line cuts \(y-\)axis at (\(0,−2\)).
⇒ \(y = \frac{6}{5}x − \frac{10}{5}\)
⇒ \(y = 1.2x − 2\)
Here, slope \(= 1.2\) and \(y-\)intercept \(= −2 \)
The line cuts \(y-\)axis at (\(0,−2\)).
2
Find two points on the line to draw the graph
When \(x = 5, y = 1.2(5) − 2= 4\)
So the point is (\(5,4\)).
When \(x = −5, y = 1.2(−5) − 2 = −8\)
So the point is (\(−5,−8\)).
So the point is (\(5,4\)).
When \(x = −5, y = 1.2(−5) − 2 = −8\)
So the point is (\(−5,−8\)).
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Final Answer : slope \(= 1.2, y-\) intercept \(= −2\), and the line cuts \(y-\) axis at (\(0,−2)\).
Concept Note
The equation of a straight line is of the form
\(y = mx + c\), where
\(m = \)slope
\(c = \)y-intercept
The values \(m\) and \(c\) completely describe the line's direction, steepness and position.