Here we will learn how to solve different types of problems on slope and yintercept.
1. (i) Determine the slope and yintercept of the line 4x + 7y + 5 = 0
Solution:
Here, 4x + 7y + 5 = 0
⟹ 7y = 4x – 5
⟹ y = \(\frac{4}{7}\)x  \(\frac{5}{7}\).
Comparing this with y = mx + c, we have: m = \(\frac{4}{7}\) and c =  \(\frac{5}{7}\)
Therefore, slope = \(\frac{4}{7}\) and yintercept =  \(\frac{5}{7}\)
(ii) Determine the slope and yintercept of the line 9x  5y + 2 = 0
Solution:
Here, 9x  5y  2 = 0
⟹ 5y = 9x + 2
⟹ y = \(\frac{9}{5}\)x + \(\frac{2}{5}\).
⟹ y = \(\frac{9}{5}\)x  \(\frac{2}{5}\).
Comparing this with y = mx + c, we have: m = \(\frac{9}{5}\) and c = \(\frac{2}{5}\)
Therefore, slope = \(\frac{9}{5}\) and yintercept = \(\frac{2}{5}\)
(iii) Determine the slope and yintercept of the line 9y + 4 = 0
Solution:
Here, 9y + 4 = 0
⟹ 9y = 4
⟹ y = \(\frac{4}{9}\)
⟹ y = 0 ∙ x \(\frac{4}{9}\)
Comparing this with y = mx + c, we have: m = 0 and c = \(\frac{4}{9}\)
Therefore, slope = 0 and yintercept = \(\frac{4}{9}\)
2. The points (2, 5) and (1, 4) are plotted in the xy plane. Find the slope and yintercept of the line joining the points.
Solution:
Let the line graph obtained by joining the points (2, 5) and (1, 4) be the graph of y = mx + c. So, the given pairs of values of (x, y) obey the relation y = mx + c.
Therefore, 5 = 2m + c ................................. (i)
4 = m + c ................................. (ii)
Subtracting (ii) from (i), we get:
5 + 4 = 2m – m
⟹ 9 = 3m
⟹ 3m = 9
⟹ m = \(\frac{9}{3}\)
⟹ m = 3
Putting m = 3 in (ii), we have: 4 = 3 + c
⟹ c = 1.
Now, m = 3 ⟹ the slope of the line graph = 3,
c = 1 ⟹ the yintercept of the line graph = 1.
On drawing the graph of y = mx + c using slope and yintercept.
3. Draw the graph of 3x  √3y = 2√3 using its slope and yintercept.
Solution:
Here, 3x  √3y = 2√3
⟹  √3y = 3x + 2√3
⟹ √3y = 3x  2√3
y = √3x – 2
Comparing with y = mx + c, we find the slope m = √3 and yintercept = 2.
Now, m = tan θ = √3
⟹ θ = 60°.
So, the graph is as shown on the above figure.
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