Question

3.a.Sketch a line through the point

Answer 1

Answer:

Step-by-step explanation:

Let the equation of the line passing through a point (x', y') and slope 'm' is,

y - y' = m(x - x')

Since x-value increases by 3,

Δx = 3

And y-value decreases by 2,

Δy = -2

Therefore, slope = $\frac{\triangle y}{\triangle x}$

Slope = $-\frac{2}{3}$

Equation of the line passing through (-2, 5) and slope = $-\frac{2}{3}$ will be,

y - 5 = $-\frac{2}{3}(x+2)$

y = $-\frac{2}{3}x-\frac{4}{3}+5$

y = $-\frac{2}{3}x+\frac{11}{3}$

y = $\frac{1}{3}(-2x+11)$

Table for input-output values will be,

x      -2         0         1          2         3

y       5        3.7       3        2.3      1.7    

We can plot these points to get the line on a graph.