Drawing Straight line graphs without a table of values grade 7

Question

I am a a student and I am having difficulty with answering this question. I keep getting the answer wrong. Please may I have a step-by-step solution to this question so that I won't have difficulties with answering these type of questions in the future.

Draw the straight line: $y = -x + 2$.

Without using a table of values.

Thank you and help would be appreciated

Answer 1

Well, what you can do is take any two points on the line, and draw a straight line right through them as follows:

Substitute any two different values of $x$ into your equation: $$y=-x+2$$ And evaluate the corresponding values of $y$.

From this, plot the two coordinates $(x,y)$ on a graph and draw a straight line through these two points.

Answer 2

Another way to do this is to inspect the equation to determine the slope, $m$, and $y-$intercept, $b$: $$y=mx+b$$

Comparing this to your equation (and rewriting slightly):

$$y=(-1)x+2$$

By inspection, the slope is $-1$ and the $y-$intercept is $2$. A slope of $-1$ means that you go down one square for each square you go to the right.

So start at the $y-$intercept $(0,2)$ and draw a line that goes northwest to southeast (slope $-1$).

Answer 3

A modest answer.

Here is a way to explain equations of straight line at $\approx$ 7th grade.

The points on the graphics below look aligned. Could you find a common property to all the displayed coordinates $(x,y)$ ? Sooner or later, one finds $x+y=2$ (btw, simpler to catch than $y=-x+2$). Let us understand why all that. A reason is that if I increase $x$ by one, I have to decrease $y$ by one in order to preserve the common property $x+y=2$, or I can increase $x$ by 2 and decrease $y$ by 2, inviting your audience to follow the moving point with a finger. This way helps in capitalizing basic linearity concepts with a natural correspondence betwen an algebraic property and a geometric property. In particular, the slope concept has been gently introduced. Then we can switch to other examples...

Back to your problem, assume you are given a straight line with equation $2x+3y=6$, that is due to cut the axes, if you do for example $y=0$ (imposing thus $2x=6$, meaning $x=3$), then you have the point $(x=3,y=0)$ which is the unique point of interection with the $x$-axis. One can do the same for $y$-axis of course.