Question

A slope of a line passing through (1,2) is -2. Then find y-intercept, equation of the line, plot the graph.

Answer 1

The line passing through (1,2) with a slope of -2 has a y-intercept of 4. Its equation is
`\(y = -2x + 4\).` The graph starts at (0,4) and slopes downward.

The equation of a line in slope-intercept form is given by
`\( y = mx + b \),`where
`\( m \)` is the slope and
`\( b \)` is the y-intercept.

Given:

- Slope
`(\( m \))` = -2

- Point
`(\( x_1, y_1 \)) = (1, 2)`

Let's find the y-intercept (\( b \)):

`\[ y_1 = mx_1 + b \]`

`\[ 2 = (-2)(1) + b \]`

`\[ 2 = -2 + b \]`

`\[ b = 4 \]`

Now, the equation of the line is:

`\[ y = -2x + 4 \]`

To plot the graph, you can use the slope and the y-intercept. Starting from the y-intercept (0,4), move down 2 units and to the right 1 unit (because the slope is -2). You can repeat this process to plot more points and draw the line. The graph passes through the point (1,2) as required.

Here's the plot:

The asterisk (*) represents the point (1,2), and the line passes through that point with a slope of -2.