Question

draw the graph of the linear equation y=mx+c for m=1/2 and c=3/2. read from the graph , the value of x,when y=4.5.

Answer 1

Here's how you find x algebraically.
y = mx + c
4.5 = x/2 + 3/2
9/2 = x/2 + 3/2
9 = x + 3
x = 6

Answer 2

Concept: A linear equation with one variable has a straight line as its graph, which can be horizontal or vertical. Any quantity added, subtracted, multiplied, or divided on both sides of a linear equation in one variable has no effect on the solution of the problem.

Given: y = mx + c ; m= $\frac{1}{2}$ and c= $\frac{3}{2}$

To find: draw the graph and the value of x when y = 4.5

Solution:

Refer the figure for the graph.

The given equation is y = mx + c

where m = $\frac{1}{2}$ and c = $\frac{3}{2}$

Therefore the equation becomes

$y = \frac{1}{2} x + \frac{3}{2}$

when x = 1, then y = $\frac{1}{2} + \frac{3}{2} = \frac{4}{2} = 2$

when x = 2, then y =

$1+\frac{3}{2} \\\\\frac{2+3}{2} \\\\\frac{5}{2} = 2.5$

when x = 3, then y =

$\frac{3}{2} + \frac{3}{2}\\\\\frac{6}{2} = 3$

so, the coordinates are (1,2), (2,2.5) and (3,3)

From the graph it is clear that when y =4.5, then x = 6.

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