The equation of the line is [tex]\boxed{y \leqslant 3}[/tex] and the passes through the point is [tex]\left( {0,3} \right).[/tex]
Further explanation:
The linear equation with slope [tex]m[/tex] and intercept [tex]c[/tex] is given as follows.
[tex]\boxed{y = mx + c}[/tex]
The formula for slope of line with points [tex]\left( {{x_1},{y_1}} \right) {\text{and} \left( {{x_2},{y_2}} \right)[/tex] can be expressed as,
[tex]\boxed{m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}}[/tex]
Given:
The passes through point are [tex]\left( {0,3} \right){\text{ and }}\left( {1,3} \right).[/tex]
Explanation:
The slope can be obtained as follows,
[tex]\begin{aligned}m&= \frac{{3 - 3}}{{1 - 0}}\\&= \frac{0}{1}\\&=0\\\end{aligned}[/tex]
Substitute [tex]0[/tex] for [tex]m[/tex], [tex]0[/tex] for [tex]x[/tex] and [tex]3[/tex] for [tex]y[/tex] in equation [tex]y = mx + c[/tex] to obtain the value of c.
[tex]\begin{aligned}3 &= 0 \cdot 0 + c\\3&=c\\\end{aligned}[/tex]
Substitute [tex]3[/tex] for [tex]c[/tex] and [tex]0[/tex] for [tex]m[/tex] in equation [tex]y = mx + c.y = 3[/tex]
The inequality is either [tex]y \geqslant 3{\text{ or }}y \leqslant 3.[/tex]
To check whether the equation includes origin substitute 0 for x and 0 for y in equation y [tex]\leqslant 3,0 \leqslant 3[/tex]
The statement is true. The equation contains origin.
The equation of the line is [tex]\boxed{y \leqslant 3}[/tex] and the passes through the point is [tex]\left( {0,3} \right).[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: numbers,slope, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation, origin.
