QUESTION 7
ii
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.
2y = 4x + 7
SOLUTION
1
Find slope and y-intercept from the given equation
\(2y = 4x + 7\)
⇒ \(y = 2x + \frac{7}{2}\)
⇒ \(y = 2x + 3.5\)
Here, slope \(= 2\) and \(y-\)intercept \(= 3.5 \)
The line cuts \(y-\)axis at (\(0,3.5\)).
⇒ \(y = 2x + \frac{7}{2}\)
⇒ \(y = 2x + 3.5\)
Here, slope \(= 2\) and \(y-\)intercept \(= 3.5 \)
The line cuts \(y-\)axis at (\(0,3.5\)).
2
Find two points on the line to draw the graph
When \(x = −1 , y = 2(−1) + 3.5 = 1.5\)
So the point is (\(−1,1.5\)).
When \(x = −2, y = 2(−2) +3.5 = −0.5\)
So the point is (\(−2,−0.5\)).
So the point is (\(−1,1.5\)).
When \(x = −2, y = 2(−2) +3.5 = −0.5\)
So the point is (\(−2,−0.5\)).
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Final Answer : slope \(= 2\), \( y-\)intercept \(= 3.5 \) and the line cuts \(y-\)axis at (\(0,3.5\)).
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.