Question

Draw the graph of the line \[x + y = 5\] . Use the graph paper drawn to find the inclination and the y-intercept of the line.
A.Slope \[ = {45^0}\] and y-intercept \[ = 5\]
B.Slope \[ = {45^0}\] and y-intercept \[ = - 5\]
C.Slope \[ = {135^0}\] and y-intercept \[ = 5\]
D.Slope \[ = {60^0}\] and y-intercept \[ = - 5\]

Answer 1

Hint: We need to draw the graph of \[x + y = 5\] . We don’t need to find all the points to draw a graph. We find the coordinates of the points at which the given line meets x-axis and y-axis. Then we stretch the line further. We can find this by putting ‘x’ is equal to zero we find the value of ‘y’ vice versa. Thus we will have two points \[(0,y)\] and \[(x,0)\] .

Complete step-by-step answer:
Given the equation of line is \[x + y = 5\] .
To find the points to draw a graph.
Put \[x = 0\] , we have
 \[ \Rightarrow 0 + y = 5\]
 \[ \Rightarrow y = 5\] .
Thus we have a coordinate point which touches the y-axis that is \[(0,5)\] .
Put \[y = 0\] we have,
 \[ \Rightarrow x + 0 = 5\]
 \[ \Rightarrow x = 5\] .
Thus we have a coordinate point which touches the x-axis that is \[(5,0)\] .
Let’s draw a graph, we have

We know that the point where a line or a curve crosses or touches the y-axis of a graph is called y-intercept. In other words we can say that the value of ‘y’ when ‘x’ is equal to zero.
In the graph we can see that the y-intercept is = 5.
Slope and inclination are both the same.
To find the slope we take the points (0, 5) and (5, 0).
We know that Slope \[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\] .
Then slope \[m = \dfrac{{0 - 5}}{{5 - 0}}\]
 \[ \Rightarrow m = \dfrac{{ - 5}}{5}\]
 \[ \Rightarrow m = - 1\]
But we know that slope is equal to tangent, that is \[m = \tan \theta \] .
Then we have \[\tan \theta = - 1\] .
We know that \[\tan ({135^0}) = \tan (90 + 45)\] \[ = - \tan (45) = - 1\] .
 \[ \Rightarrow \tan \theta = \tan ({135^0})\]
 \[\theta = {135^0}\] .
Thus the slope is \[{135^0}\] and y-intercept \[ = 5\] .
So, the correct answer is “Thus the slope is \[{135^0}\] and y-intercept \[ = 5\]”.

Note: Remember the slope formula for the two points that is \[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\] . We also know that the point where a line or a curve crosses or touches the x-axis of a graph is called the x-intercept. In other words we can say that the value of ‘x’ when ‘y’ is equal to zero. In this above problem we can tell the intercept of ‘x’ is 5.