Question

Graph the following equations of the lines: (Hint: Determine the slope and y-intercept)

Answer 1

We are given the following linear equation;

`y=-4x+5`

Note that the slope is the coefficient of x, which means, the slope of this line is -4.

Also, the y-intercept is the point where the graph crosses the y-axis, that is, the point where x = 0, then y = ?

The y-intercept here is 5.

To graph the equation, we would need to find at least two points along the line of the equation.

We can do this as follows;

`\begin{gathered} \text{When } \\ x=0 \\ y=-4x+5 \\ y=-4(0)+5 \\ y=0+5 \\ y=5 \\ So\text{ we have the point, }(0,5) \end{gathered}`

Also, we have the point;

`\begin{gathered} \text{When,} \\ x=1 \\ y=-4x+5 \\ y=-4(1)+5 \\ y=-4+5 \\ y=1 \\ We\text{ have the second point }(1,1) \end{gathered}`

Also, we have;

`\begin{gathered} \text{When} \\ x=2 \\ y=-4x+5 \\ y=-4(2)+5 \\ y=-8+5 \\ y=-3 \\ We\text{ now have }(2,-3) \end{gathered}`

Using the same procedure, we can get two more points which would be;

`\begin{gathered} (3,-7) \\ (4,-11) \end{gathered}`

We now have the following points along the line of this equation;

`(0,5),(1,1),(2,-3),(3,-7),(4,-11)`

We plot these lines on a coordinate grid (graph page) and we'll have the following;

ANSWER:

As shown above, we have the graph of the equation;

`y=-4x+5_{}`

The slope and y-intercept are;

`\begin{gathered} m=-4 \\ b=5 \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}`