Question

Draw the graph of the straight line \[y = - 2x + 3\]. Use the graph to find the intercept on the y-axis.
A) \[3\]
B) \[2\]
C) \[0\]
D) \[1\]

Answer 1

Hint: We are given here a straight line and are asked to make a graph of this straight line. We do this by taking any two points of x coordinate and then find the corresponding value for y coordinate using the given line. We thus find the two points on the Cartesian plane. We now join them to get the required line. To find the intercept on the y-axis, we see the point where the line cut the x-axis. That point will be our intercept on the y-axis.

Complete step-by-step solution:
We have the straight line \[y = - 2x + 3\]. We know that to make a straight line, we need only two points. We will then join those points, to make the straight line. To do so, we take any two values of x coordinate, say,
\[x = 0\] and\[x = 1\]. Now we put this in above equation to get the values of y for corresponding x, as,
For\[x = 0\],
\[ y = - 2 \times 0 + 3 \\
   \Rightarrow y = 3 \]
For\[x = 1\],
\[ y = - 2 \times 1 + 3 \\
   \Rightarrow y = - 2 + 3 \\
   \Rightarrow y = 1 \]
Thus we get two points as, \[(0,3),(1,1)\]. We locate this in Cartesian plane as,
 graph made using desmos.
We will now join them to the required line as,

Now to find the intercept, we look at the point where the straight line cut the y-axis. That point will be our intercept on the y-axis. That point here is \[3\].
So, the answer is A).

Note: We can also find the y intercept of the straight line with the help of graph. We know that this equation is of the intercept form of the straight line \[y = mx + b\], where \[m\] is the slope and \[b\] is the intercept on the y-axis. On comparing this with \[y = - 2x + 3\], we get the slope as \[ - 2\]and y intercept as \[3\].